Electrostatic energy, surface Coulomb

In our first simple example the electrostatic potential set up by CsCl is almost but not quite a minimal surface [10]. The reason is that the Coulomb electrostatic energy is only a part of the whole electromagnetic field. Two body, three and higher order, non-additive van der Waals interactions contribute to the complete field, distributed within the crystal. This leads one to expect that the condition that the stress tensor of the field is zero, as for soap films, yields the condition for equilibrium of the crystal. Precisely that condition is that for the existence of a minimal surface. Strictly speaking the minimal surface might be defined by the condition that the electromagnetic stress tensor is zero. But in any event, we see in this manner that the occurrence of minimal surfaces, should be a consequence of equilibrium (cf. Chapter 3,3.2.4). Indeed a statement of equilibrium may well be equivalent to quantum statistical mechanics. 

The potential due to the ionic atmosphere at the surface of the ion, i.e. at a distance a/2 from the centre of the central reference ion. Non-ideality in electrolyte solutions is a result of electrostatic interactions obeying Coulomb s Law. The potential energy of such interactions is given in terms of ... 

While there are similar mass-balance and mass-action equations in all surface complexation models, there are a great number of ways to formulate the electrostatic energy associated with adsorption on charged surfaces. Customarily the electrostatic energy of an adsorbed ion of formal charge 2 at a plane of potential is taken by Coulomb s law to be zFt/r, but the relationships used to define surface potential t/r as a function of surface charge a, or any other experimentally observable variable, are different. In addition, different descriptions of the surface/solution interface have been used, that is, division of the interface into different layers, or planes, to which different ions are assigned formally. 

There are three broad types of intermolecular forces of adhesion and cohesion (7) quantum mechanical forces, pure electrostatic forces, and polarization forces. Quantum mechanical forces account for covalent bonding. Pure electrostatic interactions include Coulomb forces between charged ions, permanent dipoles, and quadrupoles. Polarization forces arise from dipole moments induced by the electric fields of nearby charges and other permanent and induced dipoles. Ideally, the forces involved in the interaction at a release interface must be the weakest possible. These are the polarization forces known as London or dispersion forces that arise from interactions of temporary dipoles caused by fluctuations in electron density. They are common to all matter and their energies range from 0.1 to 40 kJ/mol. Solid surfaces with the lowest dispersion-force interactions are those that comprise aliphatic hydrocarbons, and fluorocarbons, and that is why such materials dominate the classification table (Table 1) and the surface energy table (Table 2). 

The electrostatic energy of the 7V-particle surface Coulomb problem, Eq. (2.1), is given explicitly by... 

The electrostatic energy, on the other hand, is not simply equal to the direct charge-charge interaction between the adsorbate and the surface atom on which it adsorbs, as assumed in Parks or MUSIC models, because of the long range of the coulomb interactions and because of the presence of the adsorbate-substrate charge transfers. Several points are worth noticing ... 

Weber and his co-workers summarized the possible interactions between solute and sorbent in adsorption as physical, chemical, and electrostatic [207], Due to the complexity of materials used and their specific characteristics (such as the presence of complexing chemical groups, small surface area, poor porosity), the sorption mechanism of polysaccharide-based materials is different from those of other conventional adsorbents. The adsorption of metal ions on adsorbent materials can be attributed to the coulombic interaction [58], The coulombic term was obtained from the electrostatic energy of interactions between the adsorbents and adsorbate. The charges on substrates as well as softness or hardness of chaige on both sides are mostly responsible for the intensity of the interaction. Coulombic interaction can be observed from adsorption of cationic species versus anionic species on adsorbents. 

---